Computer-Aided Geometric Design and Matrices

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 1926

Special Issue Editors


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Guest Editor
Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain
Interests: computer aided geometric design; approximation theory; numerical analysis; positive matrices; total positivity; high relative accuracy
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Departamento de Matemáticas, Física y Ciencias Tecnológicas, Universidad CEU Cardenal Herrera, 03203 Elche, Spain
Interests: numerical linear algebra; approximation theory; computational mathematics

Special Issue Information

Dear Colleagues,

Symmetry is a characteristic feature of geometric forms, graphics, systems, equations, matrices, and other material objects or abstract entities which is related to their invariance under certain transformations, movements, or exchanges.

Matrices are used in most areas of mathematics and in most scientific fields, either directly or through their use in geometry and numerical analysis. Many computational problems can be solved by reducing them to matrix calculus, and this often involves calculating with large-dimensional matrices. The most obvious geometric interpretation of a symmetric matrix is derived from its eigenvectors, which are orthogonal to each other, allowing for the construction of hypercubes.

Computer-aided geometric design (CAGD) is a discipline dealing with the mathematical description of shape and the computational aspects of geometric objects, of parametric curves and surfaces through control polygons and control nets.

CAGD is a field of mathematical nature, originated in naval engineering and the automotive and aircraft industries. Later, many relations arose between CAGD and other branches of mathematics.

In fact, CAGD uses tools from several mathematical fields such as differential geometry, linear algebra, computer science, numerical analysis, approximation theory and data structures.  

Nowadays, the combination of tools from matrices and CAGD is applied in computer science, many fields of engineering, industry, as well as medicine and life sciences. The main purpose of this Special Issue is to gather recent results on techniques arising from the linear algebra and computational mathematics that can be adapted to deal with problems in CAGD.

We invite you to present your recent contributions to this Special Issue.

Prof. Dr. Esmeralda Mainar
Dr. Antonio Falco
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • matrices
  • total positivity
  • high relative accuracy
  • subdivision
  • splines and NURBS
  • shape analysis
  • isogeometric analysis
  • interpolation, approximation and smoothing
  • wavelets and multi-resolution methods
  • computer graphics
  • virtual design

Published Papers (1 paper)

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Research

22 pages, 997 KiB  
Article
A New Class of Trigonometric B-Spline Curves
by Gudrun Albrecht, Esmeralda Mainar, Juan Manuel Peña and Beatriz Rubio
Symmetry 2023, 15(8), 1551; https://doi.org/10.3390/sym15081551 - 7 Aug 2023
Cited by 2 | Viewed by 1038
Abstract
We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the normalized B-basis, which has optimal shape-preserving properties and [...] Read more.
We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the normalized B-basis, which has optimal shape-preserving properties and good symmetric properties. Full article
(This article belongs to the Special Issue Computer-Aided Geometric Design and Matrices)
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